If your employer is an Indian tribe and immune from lawsuit, as a security guard does that open me up to liability?

Tribes, as quasi-independent government, have what is known as sovereign immunity: they cannot be sued in state or federal courts without their consent for many (though not all) causes of action. Some immunity may also apply to enrolled members of the tribes, at least to the extent that a cause of action arises on tribal land. However, if you are not yourself a Native American, then if you committed a tort--for example, say you used too much force or force inappropriately, and someone looked to sue you for assault--you would not be protected. You are not directly more at risk than if you worked  for a non-tribal employer--you are not any more liable as a tribe's employee than if you worked for a private company--but you may be a slightly more temptinig target to be sued: if someone is injured by a security guard, they would often sue the guard's employer, who has deeper pockets, but if your employer can't be sued for a given cause of action, the injured party might have "no choice" but to sue you to try to get some recovery.